Caption: An illustration of the surface of a sphere which is a 2-dimensional curved space. Note it is a finite, but unbounded space: there is NO boundary. The geometry of the surface is called spherical geometry.
Features:
For spherical geometry, the geodesics are great circles which are circles that cut a sphere in half. Circles that do NOT cut a sphere in half are small circles.
Airways for aviation often follow great circles on Earth at least approximately since that shortens travel distance and travel time. This is why flights from New York City to Paris often go over Greenland.
Consider the sphere in the image. Note that the equator intersects two meridians both at 90°, but they are NOT parallel elsewhere and, in fact, meet at the poles.
In Euclidean geometry, of course, geodesics (i.e., straight lines) that are parallel at one place are parallel everywhere and NEVER meet. This is the same as saying that anywhere along them there is a third geodesic that intersects them both a 90° and has the same length.
By inspection of the image, it is clear that the sum of the vertex angles for a triangle in spherical geometry is greater than 180°.